Virii defines a category of software that is comprised of viruses, worms and trojans. The general usage of the word is to describe a collection of software.
Virii itself is a plural word as there is no need for a singluar form because the more descriptive singular form of {virus, worm, or trojan} could be used.
Virii is not the plural form of virus (which is viruses). Virii has nothing to do with biological viruses.

Correct: I have a huge collection of virii!
Incorrect: I got a virii on my computer.

virii is a variant plural of the word 'virus'
It is important to note it is actually incorrect and the correct plural for 'virus' is 'viruses'
People use virii instead of viruses because
a) it looks 'better' or they want to appear of as smarter
b) they don't know it is incorrect
c) it sounds 'better' when said (vi-ree) compared to viruses (vi-rus-is)
If you use 'virii' people will announce 'your' mistake - use virii/viruses

The form virii would not have been a correct plural, since the ending -ii only occurs in the plural of masculine and feminine words ending in -ius. For instance, take radius, plural radii: the root is radi-, with the singular ending -us and the plural -i. Thus the plural virii is that of the nonexistent word virius . The form viri would also be incorrect in Latin. The ending -i is normally used for masculine or feminine nouns, not neuter ones such as virus; moreover, viri (albeit with a short i in the first syllable) is the plural of vir, and means "men."